Batch exponentiation: a fast DLP-based signature generation strategy
CCS '96 Proceedings of the 3rd ACM conference on Computer and communications security
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Improved Digital Signature Suitable for Batch Verification
IEEE Transactions on Computers
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Mix-Networks on Permutation Networks
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Use of Sparse and/or Complex Exponents in Batch Verification of Exponentiations
IEEE Transactions on Computers
A practical scheme for non-interactive verifiable secret sharing
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Accelerated verification of ECDSA signatures
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Analysis of Low Hamming Weight Products
Discrete Applied Mathematics
Batch verification of ECDSA signatures
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Batch verification suitable for efficiently verifying a limited number of signatures
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
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We propose an efficient batch verification of multiple signatures generated by different signers as well as a single signer. We first introduce a method to generate width-w Non-Adjacent Forms (w-NAFs) uniformly. We then propose a batch verification algorithm of exponentiations using w-NAF exponents, and apply this to batch verification for the modified DSA and ECDSA signatures. The performance analysis shows that our proposed method is asymptotically seven and four times as fast as individual verification in case of a single signer and multiple signers, respectively. Further, the proposed algorithm can be generalized into τ - adic w-NAFs over Koblitz curves and requires asymptotically only six elliptic curve additions per each signature for batch verification of the modified ECDSA signatures by a single singer. Our result is the first one to efficiently verify multiple signatures by multiple signers that can introduce much wider applications.